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This printable supports Common Core Mathematics Standard HSF-TF.A.1

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# Radians and Arc Length (Grades 11-12)

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## Radians and Arc Length

1.
On the unit circle (radius of 1), what is the arc length from $0deg$ to $90deg ?$
1. $90$
2. $pi/2$
3. $.25$
4. $pi$
2.
$720deg$ is equivalent to how many radians?
1. $4pi$
2. $pi/4$
3. $2pi$
4. $pi/2$
3.
Draw an angle which is $(5pi)/3$ radians and the arc which subtends it.

4.
The arc length around a unit circle has the same value as the arc angle, in radians, that it subtends.
1. True
2. False
5.
An arc length of 2.62 m on a circle with a radius of 1 m would subtend and arc angle of how many radians?
1. $pi/2$
2. $(5pi)/3$
3. $(5pi)/6$
4. $(7pi)/6$
6.
How many radians are equivalent to $315deg$?
1. $pi$
2. $(7pi)/4$
3. $(7pi)/6$
4. $(5pi)/4$
7.
Fill in the missing measurements for both degrees and radians at each blank around the unit circle. You may leave the ordered pairs blank.

8.
$45deg$ and $pi/6$ radians are equivalent angles.
1. True
2. False
9.
A circular pathway is created with a diameter of 20 feet. If the pathway makes an arc of $210deg$ how long is the pathway?
1. $210 \ "ft"$
2. $(7pi)/6$
3. $(35pi)/3 \ "ft"$
4. $35 \ "ft"$
10.
A swing at the playground is suspended by chains that are 10 feet long. Every time that a child swings from the highest point on one side to the highest point on the other side the swing travels a distance of 10.5 feet. What arc angle, in radians, is the child raveling each time the swing travels in one direction?
1. $pi/2$
2. $(3pi)/2$
3. $(2pi)/3$
4. $pi/3$
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